{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-31T02:43:47.945441Z",
     "iopub.status.busy": "2022-07-31T02:43:47.945188Z",
     "iopub.status.idle": "2022-07-31T02:43:48.038213Z",
     "shell.execute_reply": "2022-07-31T02:43:48.037510Z"
    },
    "init_cell": true,
    "origin_pos": 4,
    "slideshow": {
     "slide_type": "notes"
    },
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "from IPython import display\n",
    "import numpy as np\n",
    "import torch\n",
    "import torchvision\n",
    "from torch.utils import data\n",
    "from torchvision import transforms\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.core.interactiveshell import InteractiveShell\n",
    "InteractiveShell.ast_node_interactivity = \"all\"\n",
    "\n",
    "batch_size = 256\n",
    "# train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<div class=\"jumbotron\">\n",
    "    <p class=\"display-1 h1\">softmax回归的从零开始实现</p>\n",
    "    <hr class=\"my-4\">\n",
    "    <p>主讲：李岩</p>\n",
    "    <p>管理学院</p>\n",
    "    <p>liyan@cumtb.edu.cn</p>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# softmax回归基础"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\\begin{example}\\label{example:imageClass}\n",
    "图像分类问题：假设每次输入是一个$2\\times2$的灰度图像。\n",
    "\\begin{itemize}\n",
    "    \\item 可以用一个标量表示每个像素值，每个图像对应四个特征$x_1, x_2, x_3, x_4$。\n",
    "    \\item 假设每个图像属于类别“猫”、“鸡”和“狗”中的一个\n",
    "\\end{itemize}\n",
    "\\end{example}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\\begin{problem}\\label{prob:multioutputLabel}\n",
    "如何表示类别标签？\n",
    "\\end{problem}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\\begin{definition}\\label{def:onehot}\n",
    "**独热编码**（one-hot encoding）：是一个向量，它的分量和类别一样多；\n",
    "**类别对应的分量设置为1**，其他所有分量设置为0。\n",
    "\\end{definition}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "在Example \\ref{example:imageClass}中，标签$y$将是一个三维向量：\n",
    "- $(1, 0, 0)$对应于“猫”\n",
    "- $(0, 1, 0)$对应于“鸡”\n",
    "- $(0, 0, 1)$对应于“狗”\n",
    "\n",
    "$$y \\in \\left\\{(1, 0, 0), (0, 1, 0), (0, 0, 1)\\right\\}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 网络架构"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- 需要一个有多个输出的模型，每个类别对应一个输出"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<center><img src=\"../img/3_linear_network/softmaxreg.svg\" width=80%></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$\n",
    "\\begin{aligned}\n",
    "o_1 &= x_1 w_{11} + x_2 w_{12} + x_3 w_{13} + x_4 w_{14} + b_1,\\\\\n",
    "o_2 &= x_1 w_{21} + x_2 w_{22} + x_3 w_{23} + x_4 w_{24} + b_2,\\\\\n",
    "o_3 &= x_1 w_{31} + x_2 w_{32} + x_3 w_{33} + x_4 w_{34} + b_3.\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "用矩阵形式表达\n",
    "\n",
    "$$\n",
    "\\boldsymbol{o} = \\mathbf{W} \\boldsymbol{x} + \\boldsymbol{b}\n",
    "\\label{eq:multioutputLinear}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- softmax回归也是一个**单层神经网络**\n",
    "- softmax回归的输出层也是**全连接层**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## softmax运算"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- 希望模型的输出$\\hat{y}_j$可以视为属于类$j$的概率，然后选择具有最大输出值的类别$\\operatorname*{argmax}_j y_j$作为预测结果\n",
    "    - 例，如果$\\hat{y}_1$、$\\hat{y}_2$和$\\hat{y}_3$分别为0.1、0.8和0.1，则预测的类别是2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\\begin{problem}\\label{prob:linearProb}\n",
    "式\\eqref{eq:multioutputLinear}的结果作为概率是否可以？\n",
    "\\end{problem}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\\begin{definition}\\label{def:calibration}\n",
    "**校准**（calibration）：一个训练的目标函数，来激励模型精准地估计概率\n",
    "\\end{definition}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- **softmax**函数能够将未规范化的预测变换为**非负数并且总和为1**，同时让模型保持**可导**的性质"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$\n",
    "\\hat{\\boldsymbol{y}} = \\mathrm{softmax}(\\boldsymbol{o})\\quad\\quad \\text{其中}\\quad \\hat{y}_j = \\frac{\\exp(o_j)}{\\sum_k \\exp(o_k)}\n",
    "\\label{eq:softmaxEquation}\n",
    "$$\n",
    "\n",
    "对于所有的$j$总有$0 \\leq \\hat{y}_j \\leq 1$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "社会科学家邓肯·卢斯于1959年的离散选择模型（choice model）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- softmax运算不会改变未规范化的预测$\\boldsymbol{o}$之间的大小次序，只会确定分配给每个类别的概率"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$\n",
    "\\operatorname*{argmax}_j \\hat y_j = \\operatorname*{argmax}_j o_j\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 损失函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- 假设整个数据集$\\{\\mathbf{X}, \\mathbf{Y}\\}$具有$n$个样本，\n",
    "    - 其中索引$i$的样本由特征向量$\\boldsymbol{x}^{(i)}$和独热标签向量$\\boldsymbol{y}^{(i)}$组成"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- softmax函数给出的向量$\\hat{\\boldsymbol{y}}$可以视为“对给定任意输入$\\boldsymbol{x}$的每个类的条件概率”"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$\n",
    "P(\\mathbf{Y} \\mid \\mathbf{X}) = \\prod_{i=1}^n P(\\boldsymbol{y}^{(i)} \\mid \\boldsymbol{x}^{(i)}).\n",
    "$$\n",
    "\n",
    "其中，$\\mathbf{Y}\\in\\mathbb{R}^{n\\times q}$，$\\mathbf{X}\\in\\mathbb{R}^{n\\times d}$，表示数据集有$n$个样本，有$d$个特征，$q$个类别"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "根据最大似然估计，**最大化**$P(\\mathbf{Y} \\mid \\mathbf{X})$，相当于**最小化负对数似然**\n",
    "\n",
    "$$\n",
    "-\\log P(\\mathbf{Y} \\mid \\mathbf{X}) = \\sum_{i=1}^n -\\log P(\\boldsymbol{y}^{(i)} \\mid \\boldsymbol{x}^{(i)})\n",
    "= \\sum_{i=1}^n l(\\boldsymbol{y}^{(i)}, \\hat{\\boldsymbol{y}}^{(i)}),\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "对于任何标签$\\boldsymbol{y}$和模型预测$\\hat{\\boldsymbol{y}}$，损失函数为\n",
    "\n",
    "$$ l(\\boldsymbol{y}, \\hat{\\boldsymbol{y}}) = - \\sum_{j=1}^q y_j \\log \\hat{y}_j\n",
    "\\label{eq:crossEntropyLoss}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\\begin{definition}\\label{def:crossEntropyLoss}\n",
    "**交叉熵损失**（cross-entropy loss）：式\\eqref{eq:crossEntropyLoss}定义的损失函数\n",
    "\\end{definition}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- 交叉熵表示对于真实的概率分布$P$，用概率分布$Q$近似的时候带来的预期惊异程度\n",
    "- 符号表示为$H(P,Q)$：从$P$到$Q$的交叉熵"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$\n",
    "H(P,Q)=-\\sum_{x}P(x)\\log Q(x)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- 当$P=Q$时，交叉熵最小"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Softmax导数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- 根据softmax的定义可以得到：\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "l(\\mathbf{y}, \\hat{\\mathbf{y}}) &=  - \\sum_{j=1}^q y_j \\log \\frac{\\exp(o_j)}{\\sum_{k=1}^q \\exp(o_k)} \\\\\n",
    "&= \\sum_{j=1}^q y_j \\log \\sum_{k=1}^q \\exp(o_k) - \\sum_{j=1}^q y_j o_j\\\\\n",
    "&= \\log \\sum_{k=1}^q \\exp(o_k) - \\sum_{j=1}^q y_j o_j.\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- 对预测$o_j$的导数为\n",
    "\n",
    "$$\n",
    "\\begin{split}\n",
    "\\frac{\\partial l(\\mathbf{y}, \\hat{\\mathbf{y}})}{\\partial o_j} &= \\frac{\\exp(o_j)}{\\sum_{k=1}^q \\exp(o_k)} - y_j = \\mathrm{softmax}(\\mathbf{o})_j - y_j\\\\\n",
    "&= \\hat{y}_j-y_j.\n",
    "\\end{split}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- softmax的导数为softmax分配的概率与实际发生的情况（由独热标签向量表示）之间的差异"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 获取训练集和检验集数据"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- 使用类似MNIST（Mixed National Institute of Standards and Technology）数据集但更复杂的Fashion-MNIST数据集"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<center><img src=\"../img/3_linear_network/mnist.png\" width=80%></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Fashion-MNIST由10个类别的图像组成\n",
    "    - 每个类别由训练数据集（train dataset）中的6000张图像和测试数据集（test dataset）中的1000张图像组成"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Fashion-MNIST中包含的10个类别，分别为t-shirt（T恤）、trouser（裤子）、pullover（套衫）、dress（连衣裙）、coat（外套）、sandal（凉鞋）、shirt（衬衫）、sneaker（运动鞋）、bag（包）和ankle boot（短靴）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<center><img src=\"../img/3_linear_network/FashionMnist.png\" width=80%></center> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- 每个输入图像的高度和宽度均为28像素。 数据集由灰度图像组成，其通道数为1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 读取Fashion-MNIST数据集"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    " ```python\n",
    "import torch\n",
    "import torchvision\n",
    "from torch.utils import data\n",
    "from torchvision import transforms\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "trans = transforms.ToTensor() # 将图像数据从PIL类型变换成32位浮点数格式；不然的话，数据类型是PIL.Image.Image\n",
    "mnist_train = torchvision.datasets.FashionMNIST(\n",
    "    root=\"../data\", train=True, transform=trans, download=False)    # 创建训练集\n",
    "mnist_test = torchvision.datasets.FashionMNIST(\n",
    "    root=\"../data\", train=False, transform=trans, download=False)   # 创建检验集"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- ```python\n",
    "torchvision.datasets.FashionMNIST(root: str, train: bool = True, transform: Optional[Callable] = None, download: bool = False)\n",
    "```\n",
    "    - `root`：存储数据的根目录，`str`类型\n",
    "    - `train`：是否创建训练集，`bool`类型\n",
    "    - `transform`：将PIL图像转变为的函数\n",
    "    - `download`：是否从网络上下载数据，`bool`类型"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- PIL (Python Image Library)：`Python`的第三方图像处理库\n",
    "    - 处理栅格图像（*raster image*）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- 栅格图，也被称为位图（bitmap）、点阵图、像素图，是一个存储像素值的二维数组"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<center><img src=\"../img/3_linear_network/raster.jpg\" width=80%></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- 像素（pixel, picture element的缩写），构成栅格图的基本元素"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- 图像的深度（depth）：一个像素包含的信息量（多少个bit）\n",
    "    - 1bit，黑白图像\n",
    "    - 8bit，灰度图像，取值范围0$\\sim 2^8-1$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- 图像的分辨率（resolution）：一个图像包含的像素数量，通常表示为**长包含的像素数量$\\times$宽包含的像素数量**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- 图像的通道（channel）：图像所包含的一种主要颜色的灰度图像。在该通道上的像素值表示这种颜色的强度\n",
    "    - 例如用RGB表示的颜色，表明该图像有三通道，分别对应Red、Green、Blue三种颜色"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'训练集的长度 60000, 检验集的长度 10000'"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "'每个图像的形状 torch.Size([1, 28, 28])'"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f'训练集的长度 {len(mnist_train)}, 检验集的长度 {len(mnist_test)}'\n",
    "f'每个图像的形状 {mnist_train[0][0].shape}'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([[[0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
       "           0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
       "           0.0000, 0.0000, 0.0000, 0.0039, 0.0000, 0.0000, 0.0000, 0.0000,\n",
       "           0.0000, 0.0000, 0.0000, 0.0000],\n",
       "          [0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
       "           0.0000, 0.0000, 0.0000, 0.1725, 0.4980, 0.7137, 0.7255, 0.6314,\n",
       "           0.4706, 0.2157, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
       "           0.0000, 0.0000, 0.0000, 0.0000],\n",
       "          [0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
       "           0.0000, 0.1647, 0.7765, 0.9843, 1.0000, 0.9843, 0.9765, 0.9686,\n",
       "           1.0000, 0.9882, 0.8392, 0.3922, 0.0000, 0.0000, 0.0000, 0.0000,\n",
       "           0.0000, 0.0000, 0.0000, 0.0000],\n",
       "          [0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0078, 0.0000,\n",
       "           0.0000, 0.9137, 0.9882, 0.9294, 0.9373, 0.9176, 0.9294, 0.9216,\n",
       "           0.9294, 0.9294, 0.9961, 0.8902, 0.0000, 0.0000, 0.0000, 0.0000,\n",
       "           0.0039, 0.0000, 0.0000, 0.0000],\n",
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       "           0.0000, 0.0000, 0.0000, 0.0000],\n",
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       "           0.7922, 0.8118, 0.8078, 0.8706, 1.0000, 0.9020, 0.8627, 0.7451,\n",
       "           0.0000, 0.0000, 0.0000, 0.0000],\n",
       "          [0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.7059, 0.8863, 0.8784,\n",
       "           1.0000, 0.7804, 0.8000, 0.8118, 0.8392, 0.8392, 0.7451, 0.8471,\n",
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       "           0.0000, 0.0000, 0.0000, 0.0000],\n",
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       "           0.8118, 0.8000, 0.8157, 0.8275, 0.9765, 0.8863, 0.8392, 1.0000,\n",
       "           0.1490, 0.0000, 0.0000, 0.0000],\n",
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       "           0.3176, 0.0000, 0.0000, 0.0000],\n",
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       "           0.9412, 0.7961, 0.7843, 0.8157, 0.8078, 0.8392, 0.7569, 0.8353,\n",
       "           0.8314, 0.8157, 0.8314, 0.8275, 0.9529, 0.9490, 0.8824, 0.9961,\n",
       "           0.2588, 0.0000, 0.0000, 0.0000],\n",
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       "           0.8863, 0.7804, 0.8275, 0.7922, 0.8275, 0.8353, 0.7137, 0.8353,\n",
       "           0.8314, 0.8078, 0.7922, 0.8588, 0.8118, 0.9686, 0.8706, 0.9294,\n",
       "           0.4078, 0.0000, 0.0000, 0.0000],\n",
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       "           0.8039, 0.7804, 0.8196, 0.7922, 0.8196, 0.8275, 0.7412, 0.8392,\n",
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       "           0.5490, 0.0000, 0.0000, 0.0000],\n",
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       "           0.6510, 0.0000, 0.0000, 0.0000],\n",
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       "           0.5882, 0.7725, 0.7412, 0.8000, 0.8196, 0.8235, 0.7176, 0.8353,\n",
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       "           0.6039, 0.0000, 0.0000, 0.0000],\n",
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       "           0.5765, 0.0000, 0.0000, 0.0000],\n",
       "          [0.0000, 0.0000, 0.0000, 0.0000, 0.3569, 0.8235, 0.9020, 0.6196,\n",
       "           0.4471, 0.8039, 0.7333, 0.8157, 0.8196, 0.8078, 0.7569, 0.8235,\n",
       "           0.8275, 0.8000, 0.7647, 0.8000, 0.7098, 0.0902, 1.0000, 0.8353,\n",
       "           0.6196, 0.0000, 0.0000, 0.0000],\n",
       "          [0.0000, 0.0000, 0.0000, 0.0000, 0.3412, 0.8039, 0.9098, 0.4275,\n",
       "           0.6431, 1.0000, 0.8392, 0.8784, 0.8706, 0.8235, 0.7725, 0.8392,\n",
       "           0.8824, 0.8706, 0.8275, 0.8627, 0.8510, 0.0000, 0.9176, 0.8471,\n",
       "           0.6627, 0.0000, 0.0000, 0.0000],\n",
       "          [0.0000, 0.0000, 0.0000, 0.0000, 0.3608, 0.8353, 0.9098, 0.5725,\n",
       "           0.0196, 0.5255, 0.5922, 0.6353, 0.6667, 0.7176, 0.7137, 0.6431,\n",
       "           0.6510, 0.6980, 0.6353, 0.6118, 0.3843, 0.0000, 0.9412, 0.8824,\n",
       "           0.8235, 0.0000, 0.0000, 0.0000],\n",
       "          [0.0000, 0.0000, 0.0000, 0.0000, 0.1686, 0.6431, 0.8078, 0.5529,\n",
       "           0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
       "           0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.4980, 0.4902,\n",
       "           0.2980, 0.0000, 0.0000, 0.0000]]]),\n",
       " 4)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mnist_train[5000]  # 是一个tuple，包含2个元素，分别是图像的数据信息和图像的类别标签，标签为0～9的数字"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def get_fashion_mnist_labels(labels):  \n",
    "    ''' labels是一个标签向量（一系列类型为int的标签），把tensor([9, 0, 0, 3, 0, 2, 7, 2, 5, 5, 0, 9, 5, 5, 7, 9, 1, 0])转换为['t-shirt', 'trouser', 'pullover', 'dress', 'coat',\n",
    "                   'sandal', 'shirt', 'sneaker', 'bag', 'ankle boot']'''\n",
    "    \"\"\"返回Fashion-MNIST数据集的文本标签\"\"\"\n",
    "    text_labels = ['t-shirt', 'trouser', 'pullover', 'dress', 'coat',\n",
    "                   'sandal', 'shirt', 'sneaker', 'bag', 'ankle boot']\n",
    "    return [text_labels[int(i)] for i in labels] "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- 可视化数据集"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def show_images(imgs, num_rows, num_cols, titles=None, scale=1.5):  \n",
    "    \"\"\"绘制图像列表\"\"\"\n",
    "    figsize = (num_cols * scale, num_rows * scale)\n",
    "    _, axes = plt.subplots(num_rows, num_cols, figsize=figsize) # return figs, axes\n",
    "    axes = axes.flatten()   # 将(num_rows, num_cols)子图平展成(1, num_rows*num_cols)\n",
    "    for i, (ax, img) in enumerate(zip(axes, imgs)):\n",
    "        if torch.is_tensor(img):\n",
    "            ax.imshow(img.numpy())   # 图片张量\n",
    "        else:\n",
    "            ax.imshow(img)           # PIL图片\n",
    "        ax.axes.get_xaxis().set_visible(False)   # 隐藏横坐标\n",
    "        ax.axes.get_yaxis().set_visible(False)   # 隐藏纵坐标\n",
    "        if titles:\n",
    "            ax.set_title(titles[i])  # 给图添加标题\n",
    "    return axes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- ```python\n",
    "Axes.imshow(X)\n",
    "```\n",
    "    - `X`：图像数据，可以是`array`，形状为(M,N)，也可以是PIL图像"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "X, y = next(iter(data.DataLoader(mnist_train, batch_size=18)))  # 读取图像数据，批量为18"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'X的形状为 torch.Size([18, 1, 28, 28])，y的形状为 torch.Size([18])'"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f'X的形状为 {X.shape}，y的形状为 {y.shape}'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 972x216 with 18 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = show_images(X.reshape(18, 28, 28), 2, 9, titles=get_fashion_mnist_labels(y))\n",
    "# 显示图片\n",
    "# X.reshape(18,28,28)，改变原来X的形状，符合show_images函数要求"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 小批量读取"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- 利用`torch`内置的`DataLoader`函数批量读取数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/VENV36/lib/python3.6/site-packages/torch/utils/data/dataloader.py:481: UserWarning: This DataLoader will create 4 worker processes in total. Our suggested max number of worker in current system is 2, which is smaller than what this DataLoader is going to create. Please be aware that excessive worker creation might get DataLoader running slow or even freeze, lower the worker number to avoid potential slowness/freeze if necessary.\n",
      "  cpuset_checked))\n"
     ]
    }
   ],
   "source": [
    "batch_size = 256  # 批量大小\n",
    "\n",
    "def get_dataloader_workers():  \n",
    "    \"\"\"使用4个进程来读取数据\"\"\"\n",
    "    return 4\n",
    "\n",
    "train_iter = data.DataLoader(mnist_train, batch_size, shuffle=True,  # mnist_train类型：torchvision.datasets.mnist.FashionMNIST\n",
    "                             num_workers=get_dataloader_workers())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 完整的读取Fashion-MNIST数据集的函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- 定义`load_data_fashion_mnist`函数，用于获取和读取Fashion-MNIST数据集：\n",
    "    - 返回训练集和验证集的数据迭代器\n",
    "    - 有一个可选参数resize，可以调整图像大小"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def load_data_fashion_mnist(batch_size, resize=None):  \n",
    "    \"\"\"下载Fashion-MNIST数据集，然后将其加载到内存中\"\"\"\n",
    "    trans = [transforms.ToTensor()]   # 将图像从PIL类型转换成张量\n",
    "    if resize:\n",
    "        trans.insert(0, transforms.Resize(resize)) # resize是把小图片放大,在0之前插入\n",
    "    trans = transforms.Compose(trans)   # 组合多个transform\n",
    "    mnist_train = torchvision.datasets.FashionMNIST(\n",
    "        root=\"../data\", train=True, transform=trans, download=False)\n",
    "    mnist_test = torchvision.datasets.FashionMNIST(\n",
    "        root=\"../data\", train=False, transform=trans, download=False)\n",
    "    return (data.DataLoader(mnist_train, batch_size, shuffle=True,\n",
    "                            num_workers=get_dataloader_workers()),\n",
    "            data.DataLoader(mnist_test, batch_size, shuffle=False,\n",
    "                            num_workers=get_dataloader_workers()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- ```python\n",
    "torchvision.transforms.Resize(size)\n",
    "```\n",
    "    - 缩放给定的图像\n",
    "    - `size`：序列或者`int`\n",
    "        - 若为序列，指定缩放后的长和宽\n",
    "        - 若为`int`，图像的短边会改变到该数值，长边会被按比例缩放。例如，height>width,图像会被调整为($\\text{size}\\times\\frac{\\text{height}}{\\text{width}}$,size)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- ```python\n",
    "torchvision.transforms.Compose(transforms)\n",
    "```\n",
    "    - 组合多个transforms\n",
    "    - `transforms`：`Transform`对象的列表"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "train_iter, test_iter = load_data_fashion_mnist(32, resize=64)\n",
    "# 读取数据，批量为32，缩放到64像素"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X的形状 torch.Size([32, 1, 64, 64]), X的数据类型 torch.float32\n",
      " y的形状 torch.Size([32]), y的数据类型 torch.int64\n"
     ]
    }
   ],
   "source": [
    "for X, y in train_iter:\n",
    "    print(f'X的形状 {X.shape}, X的数据类型 {X.dtype}\\n y的形状 {y.shape}, y的数据类型 {y.dtype}')\n",
    "    break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 实现softmax函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- 用Fashion-MNIST数据集实现softmax分类算法\n",
    "- 批量设置为256"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "batch_size = 256  # 批量大小\n",
    "train_iter, test_iter = load_data_fashion_mnist(batch_size)   #读取批量数据"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 初始化模型参数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- 每个样本都将用固定长度的向量表示\n",
    "    - 原始数据集中的每个样本都是$28 \\times 28$的图像，在此**将展平每个图像，把它们看作长度为784的向量**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- 数据集有10个类别，所以网络输出维度为10\n",
    "- 权重将构成一个$784 \\times 10$的矩阵\n",
    "- 偏置将构成一个$1 \\times 10$的行向量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "num_inputs = 784 # 1*28*28 = 784\n",
    "num_outputs = 10\n",
    "\n",
    "# 初始化模型参数\n",
    "W = torch.normal(0, 0.01, size=(num_inputs, num_outputs), requires_grad=True)  # 初始化权重，服从正态分布N(0,0.01)\n",
    "b = torch.zeros(num_outputs, requires_grad=True)   # 初始化偏置为0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 定义softmax操作"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- 对每个项指数运算（使用`exp`）；\n",
    "- 对每一行求和（小批量中每个样本是一行），得到每个样本的规范化常数；\n",
    "- 将每一行除以其规范化常数，确保结果的和为1。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$\n",
    "\\mathrm{softmax}(\\mathbf{X})_{ij} = \\frac{\\exp(\\mathbf{X}_{ij})}{\\sum_k \\exp(\\mathbf{X}_{ik})}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-31T02:43:48.060001Z",
     "iopub.status.busy": "2022-07-31T02:43:48.059778Z",
     "iopub.status.idle": "2022-07-31T02:43:48.063891Z",
     "shell.execute_reply": "2022-07-31T02:43:48.063262Z"
    },
    "origin_pos": 14,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def softmax(X): # X的行数是样本数，因此每行有10个X_k,转成10个和为1的概率数\n",
    "    X_exp = torch.exp(X)\n",
    "    partition = X_exp.sum(dim=1, keepdim=True)\n",
    "    return X_exp / partition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- ```python\n",
    "torch.sum(input,dim,keepdim=False)\n",
    "```\n",
    "    - 给定一个矩阵`input`，可以对所有元素求和\n",
    "    - 也可以只求同一个轴上的元素之和，即同一列（轴0）或同一行（轴1），用参数`dim`设定\n",
    "    - 若按轴求和，求和之后这个轴的元素个数为１，所以对应的维度会被去掉，如果要保留这个维度，则应当`keepdim=True`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-31T02:43:48.048976Z",
     "iopub.status.busy": "2022-07-31T02:43:48.048601Z",
     "iopub.status.idle": "2022-07-31T02:43:48.056970Z",
     "shell.execute_reply": "2022-07-31T02:43:48.056335Z"
    },
    "origin_pos": 10,
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[1., 2., 3.],\n",
       "        [4., 5., 6.]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = torch.tensor([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[5., 7., 9.]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "tensor([[ 6.],\n",
       "        [15.]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.sum(0, keepdim=True) # 按轴求和之后保留维度，keepdim=True\n",
    "X.sum(1, keepdim=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([5., 7., 9.])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "tensor([ 6., 15.])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.sum(0)   # 按轴求和后未保留维度\n",
    "X.sum(1)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "检验一下定义的softmax函数是否运行正确"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-31T02:43:48.066702Z",
     "iopub.status.busy": "2022-07-31T02:43:48.066485Z",
     "iopub.status.idle": "2022-07-31T02:43:48.072898Z",
     "shell.execute_reply": "2022-07-31T02:43:48.072285Z"
    },
    "origin_pos": 16,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[ 1.2986,  0.8923,  1.0202,  0.1019,  0.1728],\n",
       "        [-1.1082, -1.8321, -0.7797, -1.2621, -0.4108]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X1 = torch.normal(0, 1, (2, 5))  # 生成一个2行5列的服从正态分布N(0,1)的矩阵\n",
    "X1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X1每个元素对应的概率为\n",
      "tensor([[0.3279, 0.2184, 0.2482, 0.0991, 0.1064],\n",
      "        [0.1742, 0.0845, 0.2420, 0.1494, 0.3499]])\n",
      " X1每行求和tensor([1.0000, 1.0000])\n"
     ]
    }
   ],
   "source": [
    "X1_prob = softmax(X1)\n",
    "print(f'X1每个元素对应的概率为\\n{X1_prob}\\n X1每行求和{X1_prob.sum(1)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 建立softmax回归模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-31T02:43:48.075677Z",
     "iopub.status.busy": "2022-07-31T02:43:48.075461Z",
     "iopub.status.idle": "2022-07-31T02:43:48.079250Z",
     "shell.execute_reply": "2022-07-31T02:43:48.078602Z"
    },
    "origin_pos": 19,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def net(X):\n",
    "    return softmax(torch.matmul(X.reshape((-1, W.shape[0])), W) + b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- 注意：`W`的形状是$784\\times10$，因此用`reshape`将每张原始图像数据（$28\\times28$）展平成一个长度为784向量"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 定义损失函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- 实现交叉熵损失函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-31T02:43:48.091932Z",
     "iopub.status.busy": "2022-07-31T02:43:48.091398Z",
     "iopub.status.idle": "2022-07-31T02:43:48.097732Z",
     "shell.execute_reply": "2022-07-31T02:43:48.097055Z"
    },
    "origin_pos": 24,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def cross_entropy(y_hat, y):\n",
    "    \"\"\"\n",
    "        y_hat：预测值\n",
    "        y：真值\n",
    "    \"\"\"\n",
    "    return - torch.log(y_hat[range(len(y_hat)), y])  # torch.log是以自然数e为底的对数函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- 创建一个数据样本`y_hat`，其中包含2个样本在3个类别的预测概率，以及它们对应的标签`y`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-31T02:43:48.082190Z",
     "iopub.status.busy": "2022-07-31T02:43:48.081700Z",
     "iopub.status.idle": "2022-07-31T02:43:48.087699Z",
     "shell.execute_reply": "2022-07-31T02:43:48.087051Z"
    },
    "origin_pos": 21,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y_hat为\n",
      "tensor([[0.1000, 0.3000, 0.6000],\n",
      "        [0.3000, 0.2000, 0.5000]])\n",
      "y为 tensor([0, 2])\n"
     ]
    }
   ],
   "source": [
    "y_hat = torch.tensor([[0.1, 0.3, 0.6], [0.3, 0.2, 0.5]])\n",
    "y = torch.tensor([0, 2]) # 在第一个样本中，第1类是正确的预测； 而在第二个样本中，第3类是正确的预测\n",
    "print(f'y_hat为\\n{y_hat}')\n",
    "print(f'y为 {y}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- 使用y作为y_hat中概率的索引， 选择第一个样本中第1类的概率和第二个样本中第3类的概率"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.1000, 0.5000])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_hat[[0, 1], y] #【0，1】是样本序列，y是每个样本对应的真实分类标号"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([2.3026, 0.6931])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 计算y_hat和y的交叉熵\n",
    "cross_entropy(y_hat, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 评估准确率"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- 分类须输出硬预测（hard prediction）时， 通常选择预测概率最高的类"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- 将预测类别与真实`y`元素进行比较，当预测与标签分类y一致时，即是正确的"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\\begin{definition}\\label{def:accuracy}\n",
    "分类精度：正确预测数量与总预测数量之比\n",
    "\\end{definition}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### 实现计算分类精度的函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- y_hat是矩阵，假定第二个维度存储每个类的预测分数\n",
    "- 使用argmax获得每行中最大元素的索引来获得预测类别"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-31T02:43:48.109842Z",
     "iopub.status.busy": "2022-07-31T02:43:48.109628Z",
     "iopub.status.idle": "2022-07-31T02:43:48.114858Z",
     "shell.execute_reply": "2022-07-31T02:43:48.114250Z"
    },
    "origin_pos": 29,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def accuracy(y_hat, y):  \n",
    "    \"\"\"计算预测正确的数量\"\"\"\n",
    "    if len(y_hat.shape) > 1 and y_hat.shape[1] > 1:  #判断y_hat是一个矩阵\n",
    "        y_hat = y_hat.argmax(axis=1)  # torch.argmax\n",
    "    cmp = y_hat.type(y.dtype) == y    # 因为运算符==对数据类型敏感，将y_hat转换成与y相同的数据类型，便于比较\n",
    "    return float(cmp.type(y.dtype).sum()) # cmp是bool向量，转换为与y相同的数据类型，可以求和"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- ```python\n",
    "torch.argmax(input, dim)\n",
    "```\n",
    "    - 返回指定维度上最大值的序号\n",
    "    - `input`输入张量\n",
    "    - `dim`指定的维度（轴）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- ```python\n",
    "torch.Tensor.type(dtype=None)\n",
    "```\n",
    "    - `dtype`：需要的数据类型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "预测值为\n",
      "tensor([[0.1000, 0.3000, 0.6000],\n",
      "        [0.3000, 0.2000, 0.5000]])\n",
      "真值为tensor([0, 2])\n"
     ]
    }
   ],
   "source": [
    "print(f'预测值为\\n{y_hat}')\n",
    "print(f'真值为{y}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- 第一个样本的预测类别是2，与真值**不符**\n",
    "- 第二个样本的预测类别是2，与真值**相符**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'分类的精度为0.5'"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 在假想的预测值y_hat和真值y上的分类精度为\n",
    "f'分类的精度为{accuracy(y_hat, y) / len(y)}'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### 实现计算数据迭代器可访问数据集的分类精度"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- 需要累计在每个批量上**预测正确的数量**与**预测的总数量**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- 定义`Accumulator`类\n",
    "    - 创建2个变量，分别用于存储正确预测的数量和预测的总数量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-31T02:43:48.136354Z",
     "iopub.status.busy": "2022-07-31T02:43:48.135880Z",
     "iopub.status.idle": "2022-07-31T02:43:48.667940Z",
     "shell.execute_reply": "2022-07-31T02:43:48.666945Z"
    },
    "origin_pos": 36,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "class Accumulator:  \n",
    "    \"\"\"在n个变量上累加\"\"\"\n",
    "    def __init__(self, n):\n",
    "        self.data = [0.0] * n  # 生成初始值为0的含n个元素的列表\n",
    "\n",
    "    def add(self, *args):\n",
    "        # 对n个变量分别累加\n",
    "        self.data = [a + float(b) for a, b in zip(self.data, args)]\n",
    "\n",
    "    def reset(self):\n",
    "        self.data = [0.0] * len(self.data)\n",
    "\n",
    "    def __getitem__(self, idx):\n",
    "        return self.data[idx]   # 类中定义__getitem__函数，可以获取指定序号的数据"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- 构建可以评估任意模型`net`分类精度的函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-31T02:43:48.118510Z",
     "iopub.status.busy": "2022-07-31T02:43:48.118292Z",
     "iopub.status.idle": "2022-07-31T02:43:48.123338Z",
     "shell.execute_reply": "2022-07-31T02:43:48.122692Z"
    },
    "origin_pos": 32,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def evaluate_accuracy(net, data_iter):  \n",
    "    \"\"\"计算在指定数据集上模型的精度\"\"\"\n",
    "    if isinstance(net, torch.nn.Module):\n",
    "        net.eval() # 将模型设置为评估模式\n",
    "    metric = Accumulator(2) # 需要累计2个变量：正确预测数 和 预测总数\n",
    "    with torch.no_grad():   # 不需要计算梯度\n",
    "        for X, y in data_iter:\n",
    "            metric.add(accuracy(net(X), y), y.numel())\n",
    "    return metric[0] / metric[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0918"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 在给定的初始权重和偏置，构建的softmax回归模型的初始分类精度为\n",
    "evaluate_accuracy(net, test_iter)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 建立优化器"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- 小批量随机梯度下降优化模型的损失函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def sgd(params, lr, batch_size):  # params: [w,b]\n",
    "    \"\"\"小批量随机梯度下降\n",
    "    lr：学习速率\n",
    "    \"\"\"\n",
    "    with torch.no_grad(): # 在该上下文管理器下，所有计算得出的tensor的requires_grad都自动设置为False。\n",
    "        for param in params:\n",
    "            param -= lr * param.grad / batch_size  # 更新参数，学习速率lr控制更新大小，批量大小batch_size规范化步长\n",
    "            param.grad.zero_() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "lr = 0.1  # 学习速率\n",
    "\n",
    "def updater(batch_size):\n",
    "    return sgd([W, b], lr, batch_size)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Softmax回归的训练"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "## 定义一个函数来训练一个迭代周期"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-31T02:43:48.672101Z",
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     "shell.execute_reply": "2022-07-31T02:43:48.680765Z"
    },
    "origin_pos": 39,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def train_epoch_ch3(net, train_iter, loss, updater):  \n",
    "    \"\"\"训练模型一个迭代周期（定义见第3章）\n",
    "    net: 模型网络\n",
    "    train_iter: 训练数据迭代器\n",
    "    loss：损失函数\n",
    "    updater：优化器\n",
    "    \"\"\"\n",
    "    if isinstance(net, torch.nn.Module):\n",
    "        # 将模型设置为训练模式\n",
    "        net.train()\n",
    "    metric = Accumulator(3) #累计3个变量：# 训练损失总和、训练准确度总和、样本数\n",
    "    for X, y in train_iter:\n",
    "        y_hat = net(X)  # 计算梯度并更新参数，得到预测值\n",
    "        l = loss(y_hat, y)  # 计算损失\n",
    "        if isinstance(updater, torch.optim.Optimizer):\n",
    "            # 使用PyTorch内置的优化器和损失函数\n",
    "            updater.zero_grad()\n",
    "            l.mean().backward()  # 反向计算梯度，注意pytorch内置优化器用mean函数将损失向量变为标量\n",
    "            updater.step()       # 更新参数\n",
    "        else:\n",
    "            # 使用自己定制的优化器和损失函数\n",
    "            l.sum().backward()\n",
    "            updater(X.shape[0])\n",
    "        metric.add(float(l.sum()), accuracy(y_hat, y), y.numel())\n",
    "    # 返回训练损失和分类精度\n",
    "    return metric[0] / metric[2], metric[1] / metric[2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 定义一个动画绘制训练过程的类"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-31T02:43:48.684252Z",
     "iopub.status.busy": "2022-07-31T02:43:48.684046Z",
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     "shell.execute_reply": "2022-07-31T02:43:48.693295Z"
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    "origin_pos": 42,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "class Animator:  \n",
    "    \"\"\"在动画中绘制训练过程\"\"\"\n",
    "    def __init__(self, xlabel=None, ylabel=None, legend=None, xlim=None,\n",
    "                 ylim=None, xscale='linear', yscale='linear',\n",
    "                 fmts=('-', 'm--', 'g-.', 'r:'), nrows=1, ncols=1,\n",
    "                 figsize=(3.5, 2.5)):\n",
    "        if legend is None:\n",
    "            legend = []\n",
    "        use_svg_display()  # 用矢量图显式\n",
    "        self.fig, self.axes = plt.subplots(nrows, ncols, figsize=figsize)\n",
    "        if nrows * ncols == 1:\n",
    "            self.axes = [self.axes, ]\n",
    "        # 使用lambda函数捕获参数，设置轴的属性\n",
    "        self.config_axes = lambda: set_axes(\n",
    "            self.axes[0], xlabel, ylabel, xlim, ylim, xscale, yscale, legend)\n",
    "        self.X, self.Y, self.fmts = None, None, fmts\n",
    "\n",
    "    def add(self, x, y):\n",
    "        # 向图表中添加多个数据点\n",
    "        if not hasattr(y, \"__len__\"):\n",
    "            y = [y]  # 变成列表，以便下方取y的长度\n",
    "        n = len(y)\n",
    "        if not hasattr(x, \"__len__\"):\n",
    "            x = [x] * n\n",
    "        if not self.X:\n",
    "            self.X = [[] for _ in range(n)]\n",
    "        if not self.Y:\n",
    "            self.Y = [[] for _ in range(n)]\n",
    "        for i, (a, b) in enumerate(zip(x, y)):\n",
    "            # 相同的x与每个y匹配（每个y代表一类数据，例如训练损失、训练分类精度、检验分类精度）\n",
    "            if a is not None and b is not None:\n",
    "                self.X[i].append(a)\n",
    "                self.Y[i].append(b)\n",
    "        self.axes[0].cla()  # 清除轴\n",
    "        for x, y, fmt in zip(self.X, self.Y, self.fmts):\n",
    "            self.axes[0].plot(x, y, fmt)\n",
    "        self.config_axes()\n",
    "        display.display(self.fig)\n",
    "        display.clear_output(wait=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "from IPython import display\n",
    "\n",
    "def use_svg_display():\n",
    "    # 显式矢量图在Jupyter中显式绘图\n",
    "    display.set_matplotlib_formats('svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def set_axes(axes, xlabel, ylabel, xlim, ylim, xscale, yscale, legend):\n",
    "    \"\"\"设置matplotlib的轴\"\"\"\n",
    "    axes.set_xlabel(xlabel)  # 设置x标签\n",
    "    axes.set_ylabel(ylabel)\n",
    "    axes.set_xscale(xscale)  # 设置x轴的比例\n",
    "    axes.set_yscale(yscale)\n",
    "    axes.set_xlim(xlim)      # 设置x轴的范围\n",
    "    axes.set_ylim(ylim)\n",
    "    if legend:\n",
    "        axes.legend(legend)  # 增添图例\n",
    "    axes.grid()              # 打开网格"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 训练函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- 会在`train_iter`访问到的训练数据集上训练一个模型`net`\n",
    "- 训练函数会运行多个迭代周期（由`num_epochs`指定）\n",
    "- 利用`Animator`类来可视化训练进度"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-31T02:43:48.696646Z",
     "iopub.status.busy": "2022-07-31T02:43:48.696446Z",
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     "shell.execute_reply": "2022-07-31T02:43:48.701136Z"
    },
    "origin_pos": 44,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def train_ch3(net, train_iter, test_iter, loss, num_epochs, updater):  \n",
    "    \"\"\"训练模型（定义见第3章）\"\"\"\n",
    "    animator = Animator(xlabel='epoch', xlim=[1, num_epochs], ylim=[0.3, 0.9],\n",
    "                        legend=['train loss', 'train acc', 'test acc'])\n",
    "    for epoch in range(num_epochs):\n",
    "        train_metrics = train_epoch_ch3(net, train_iter, loss, updater)\n",
    "        # 评估在检验集上的分类精度\n",
    "        test_acc = evaluate_accuracy(net, test_iter)\n",
    "        # 横轴是迭代周期、纵轴包括三个值：训练损失、训练分类精度、检验分类精度\n",
    "        # train_metrics是一个tuple，+(test_acc,)构成三个值的tuple\n",
    "        animator.add(epoch + 1, train_metrics + (test_acc,))\n",
    "    train_loss, train_acc = train_metrics\n",
    "    assert train_loss < 0.5, train_loss\n",
    "    assert train_acc <= 1 and train_acc > 0.7, train_acc\n",
    "    assert test_acc <= 1 and test_acc > 0.7, test_acc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- 训练模型10个迭代周期"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-31T02:43:48.710770Z",
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     "shell.execute_reply": "2022-07-31T02:44:21.176306Z"
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    "origin_pos": 49,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
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   "source": [
    "num_epochs = 10\n",
    "train_ch3(net, train_iter, test_iter, cross_entropy, num_epochs, updater)"
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  {
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   "source": [
    "## 对图像进行分类预测"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-31T02:44:21.180478Z",
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    "origin_pos": 51,
    "slideshow": {
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    },
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def predict_ch3(net, test_iter, n=6):  \n",
    "    \"\"\"预测标签\n",
    "    n：显示图像的数量\n",
    "    \"\"\"\n",
    "    for X, y in test_iter:\n",
    "        break\n",
    "    trues = get_fashion_mnist_labels(y)   # 获得真实类别对应的类别名称\n",
    "    # net(X).argmax(axis=1) 获得数据的硬预测\n",
    "    preds = get_fashion_mnist_labels(net(X).argmax(axis=1))\n",
    "    titles = [true +'\\n' + pred for true, pred in zip(trues, preds)]   # 真实和预测值对应的类别名称构成的列表\n",
    "    _ = show_images(X[0:n].reshape((n, 28, 28)), 1, n, titles=titles[0:n])  # 1行n列，注意改变图像数据的形状，去除通道维度"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
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